He does not expect Arsenal, under the new Unai Emery regime, to have enough to challenge for a return to Champions League football.
He expects Liverpool FC and Manchester City to take the two top spots and said United need to address the disharmony surrounding them to achieve their goals.
“Manchester United would have to address this disharmony within the squad,” he said to the Daily Express.
“They’ve got a top squad and manager, but the harmony isn’t great.
“It’s going to be between Tottenham, Chelsea and United.
“Liverpool and City will be in there [the top four].”
Barnes won the old First Divison with Liverpool FC the last time they won it 30 years ago but only backs his former club to be near enough Manchester City this season to guarantee Champions League football.
Arch-rivals Manchester United have won just two of their opening four games this season, losing the other two.
Barnes has said United will need to address their off-the-field problems if they are to challenge for the top four.
Tottenham who bested United 3-0 at Old Trafford in August, will apparently also be in for a scrap if they are to retain Champions League football.
Barnes believes Chelsea FC will also be left to battle it out for the final two top-four spots, despite the Blues winning all four of their games this season and sitting joint-top of the Premier League.
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